Related papers: Time Scale Calculus: A New Approach to Multi-Dose …

To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories". Examples of such descriptions include the…

A lot of criticism against the standard formulation of pharmacokinetics has been raised by several authors. It seems that the natural reaction for that criticism is to comment it from the point of view of the theory of conservation laws.…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Time series models such as dynamical systems are frequently fitted to a cohort of data, ignoring variation between individual entities such as patients. In this paper we show how these models can be personalised to an individual level while…

Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…

A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…

We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…

The objective of the present paper is to use the well known Ross-Macdonald models as a prototype, incorporating spatial movements, identifying different times scales and proving a singular perturbation result using a system of local and…

In this paper, we investigate the problem of Model Predictive Control (MPC) of dynamic systems for high-level specifications described by Signal Temporal Logic (STL) formulae. Recent works show that MPC has the great potential in handling…

Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…

Time Series Classification (TSC) involved building predictive models for a discrete target variable from ordered, real valued, attributes. Over recent years, a new set of TSC algorithms have been developed which have made significant…

Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…

Model Predictive Control (MPC) has established itself as the primary methodology for constrained control, enabling autonomy across diverse applications. While model fidelity is crucial in MPC, solving the corresponding optimization problem…

Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality…

Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data…

Current mathematical frameworks for predicting the flux state and macromolecular composition of the cell do not rely on thermodynamic constraints to determine the spontaneous direction of reactions. These predictions may be biologically…

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…

We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…